The regularizing properties of the adjoint gradient method in ill-posed problems
USSR Computational Mathematics and Mathematical Physics
Fundamentals of digital image processing
Fundamentals of digital image processing
Optimal and superoptimal circulant preconditioners
SIAM Journal on Matrix Analysis and Applications
FFT-based preconditioners for Toeplitz-block least squares problems
SIAM Journal on Numerical Analysis
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Superoptimal Preconditioned Conjugate Gradient Iteration for Image Deblurring
SIAM Journal on Scientific Computing
Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory)
| Hi-index | 0.00 |
In this paper we study a fast deconvolution technique for the image restoration problem of the Large Binocular Telescope (LBT) interferometer. Since LBT provides several blurred and noisy images of the same object, it requires the use of multiple-image deconvolution methods in order to produce a unique image with high resolution. Hence the restoration process is basically a linear ill-posed problem, with overdetermined system and data corrupted by several components of noise. Here the preconditioned conjugate gradient method is used to obtain regularized reconstructions within few iterations. In particular, we study the effectiveness of some preconditioners which have been previously proposed for discrete ill-posed problems. These preconditioners can be considered as regularizing tools since they are able to increase the speed of convergence without amplifying the reconstruction from components with high noise. A wide set of numerical tests will confirm the useful properties of the technique.